A pro-government Ethiopian militia commander alleged on Tuesday that Tigrayan rebel leaders were now in Eritrea, a claim that was immediately denied by the Eritrean minister for information.
AFP was not able to immediately verify the claims.
The Tigray People's Liberation Front (TPLF), which has run the region for years, launched an offensive against the government last month, but was ultimately forced to retreat and lost control of the state.
The fighting raised fears of a regional war, as the rebels had the backing of neighbouring Eritrea, which deployed thousands of troops in Ethiopian territory. But they were also forced to retreat after repeated drone attacks.
Ethiopia and Eritrea severed diplomatic relations in October, with each side accusing the other of attempting to destabilise it.
"TPLF leaders crossed the border into Eritrea," Gebregziabher Beyene, a commander with the pro-government Tigray Peace Force (TPF), said Tuesday.
Gebregziabher made the remarks while addressing residents of Mekelle, the capital of Tigray, which fell to federal forces earlier this month.
He also claimed TPLF leaders took a "large amount of military equipment and medicines" to the Eritrean capital Asmara.
The commander's claims were immediately disputed by Eritrean Information Minister Yemane Gebremeskel, who dismissed them as "lies".
TPLF vice president Amanuel Assefa also denied the comments, telling AFP: "The leadership is working within Tigray."
Gebregziabher was appointed by the federal government on Friday as part of an interim administration in Tigray, tasked with organising elections within six months.
The enmity between Ethiopia and Eritrea, which achieved independence in 1993 and has been led by Isaias Afwerki since, is long-lasting.
The two countries fought a 1998-2000 border war, costing tens of thousands of lives.
A brief detente from 2019 ended after the 2020-22 Tigray war, during which Eritrean troops fought alongside federal forces against rebels, over dissatisfaction with the peace terms.
Ethiopia claims Eritrea is supporting the TPLF, while Eritrea accuses its landlocked neighbour of coveting the Eritrean port of Assab.
The international community has voiced increasing concern about the risk of a new war.